Question: Solve for $x$ and $y$ using elimination. ${-3x+y = -16}$ ${5x+2y = 34}$
Answer: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the top equation by $-2$ ${6x-2y = 32}$ $5x+2y = 34$ Add the top and bottom equations together. $11x = 66$ $\dfrac{11x}{{11}} = \dfrac{66}{{11}}$ ${x = 6}$ Now that you know ${x = 6}$ , plug it back into $\thinspace {-3x+y = -16}\thinspace$ to find $y$ ${-3}{(6)}{ + y = -16}$ $-18+y = -16$ $-18{+18} + y = -16{+18}$ ${y = 2}$ You can also plug ${x = 6}$ into $\thinspace {5x+2y = 34}\thinspace$ and get the same answer for $y$ : ${5}{(6)}{ + 2y = 34}$ ${y = 2}$